Start by patting your fish dry with paper towels to remove any excess moisture. This helps in achieving a lovely sear. Season both sides lightly with salt and pepper.
In your heavy-bottomed skillet, melt 4 ounces of the unsalted butter over low heat. You want it to melt gently without browning.
Once the butter is melted, add the finely diced shallots to the skillet. Sauté for about 2-3 minutes until they become translucent and fragrant.
Carefully place the fish into the skillet, making sure it’s submerged in the melted butter. Cook for about 8-10 minutes, depending on the thickness of the fish. The fish is done when it flakes easily with a fork and reaches an internal temperature of 145°F (63°C).
Once the fish is cooked, remove the skillet from heat and stir in the remaining 2 ounces of butter, lemon juice, and any finely chopped fresh herbs you’re using. Spoon the buttery sauce over the fish to coat it well.
Using tongs or a spatula, carefully transfer the fish to serving plates. Drizzle with additional sauce and garnish with more herbs if desired. Serve immediately and enjoy the rich flavors of your butter poached fish!